Wave filter



May 26, 1925.

1,538,964 0. .J. ZOBEL WAVE FILTER Filed Jan. 15, 1921 5 Sheets-Sheet 1 anomtoz (9150 JZv'eZ $51 Momma May 26, 1925. 1,538,964

- 0. J. ZOBEL WAVE FILTER .Filed'Jap. 15, 1921, 5 Sheets-Sheet 2 avwemtoz (91.7011 Zak/ 5 53513 flT/tovmm May 26, 1925. 'L538 94 OI J. ZOBEL WAVE FILTER Filed Jan. 15, 1921 5 Sheets-Sheet 4 wumtoz Patented May 26, 1925.

OTTO .1. zoBnL, or new onx,

N. Y., ASSIGNOR TO AMERICAN TELEPHONE AND TELEGRAPH COMPANY, A OORl-ORATION OF NEW YORK.

WAVE FILTER Application filed January 15, 1921. Serial 1T0. 487,527.

7 '0 all whom it may concern:

Be it known that I, O'rro J. ZoBEL, residing at New York, in the county of New York and State of New York, have invented certain Improvements in Wave Filters, of which the following is a specification.

The principal object of my invention is to provide a. new and improved network for the purpose of transmitting electric cur rents having their frequency Within a certain range and attenuating currents of frequency within a different range. My improvement belongs to the class of devices commonly called wave-filters and I shall refer to them by that name. Another object of my invention is to provide a Wavefilter with recurrent sections not all of which are alike, and having certain advantages over a wave-filter with all its sections alike. Another object of my invention is to provide a class of wave-filters which shall be alike as to the transition frequencies between the free transmitting ranges and the attenuating ranges, but shall be unlike in other respects, so that a choice may be made among them as to the one most desirable for the attainment of a given object for which these wave-filters may be employed. Another object of my invention is to provide a tapered wave-filter which may go in between lines or apparatus of different characteristic impedances so as to transmit. currents without serious reflection losses. These and other objects, of my invention will be made apparent by the following discussion of a few specific embodiments of the inventive idea.

The following specification relates specifically to examples chosen by way of illustration, and the definition of my invention will be given in the appended claims.

Referring to the drawings, Figure 1 is a diagram illustrating a Wave-filter of known type with the recurrent sections all having their corresponding component inipedance alike. Fig. 2 is a diagram showing a derived S-type Wave-filter for which the prototype is given in Fig. 1. (The use of the term Sty'peand similar terms will be explained later.) Fig. 3 is a diagram illustrating an H-type wave filter derived from Fig. 1 as the prototype. Fig. 4 is a curve diagram exhibiting attenuation characteristics for the wave-filters of F igs. 2 and 3, each of which includes Fig.1 as

a limiting case. Fig. 5 is a. diagram illustratin two complementary wave-filters on a sing e input line. Figs. 6 and 7 are diagrams giving attenuation characteristics for the two wave-filters of Fig. 5. Fig. 8 is a d 1agram corresponding to Fig. 5, but exhibitmg the replacement of certain of the wave-filter sections of Fig. 5 by S-type sections, for a purpose that will be explained later. Figs. 9, 10 and 11 arediagrams illustrating the introduction of a half S-type section at the input termination of a wavefiltcr to serve as a reactance annulling network, and to give 'a substantially constant resistance over the freetransmitting range. Fig. 12 is a tapered wave-filter whose sections are all derived as S-types from a common initial prototype. diagrams illustrating steps in the develop-' ment of the theory of the tapered Wavefilter shown in Fig. 12. Figs. 15, 16 and 17 are diagrams of other forms of tapered The known general type of wave-filter, of which my improved wave-filter may be regarded as a development, is illustrated in Fig. 1, which shows a periodically recurring network with the series impedances z, and the periodically recurring shunt impedances 2 One series impedance 2, has been divided into two equal parts with the point A between them to facilitate definition of the mid-series termination. If the wave-filter is cut off at A and B, its impedance looking to the right is called the mid-series characteristic impedance, and is represented by Z In this case the wavefilter is said to have mid-series termina- -t1on.

One shunt impedance 2, has been substituted by the equivalent combination oftwo shunt impedances in arallel, each of value 22 on either side of the points 0 and D. This aflords an opportunity to explain the term mid-shunt termination. If the wave-filter is cut off at the points C and D, the part looking to the right is said to have mid-shunt termination, and its impedance Z is called the mid-shunt characteristic impedance.

The theory of this wave-filter is usually developed most readily on the assumption, that the number of sections to the right of the termination, whether mid-series at AB or mid-Shunt at CD, is infinite. A moder- Figs. 13 and 14are t I r e fe rence to its prototype by the equations. 2, ='==s2 (1) and Before entering upon a discussion of the properties and uses of S-type wave-filters and wave-filter sections, I will define the H-type. With Fig. 1 as the prototype, an H-t pe wave-filter is shown in Fig. 3, where 1 co With reference to the prototype in Fig. 1, the H-type wave-filter is completely defined by the equations 1 n-1 1 (3) 2 ehz,

Before exhibiting the use that may be made of wave-filters and wave-filter sections of S- and H-types, I will direct attention to some of their properties upon which their utility depends.

With mid-series termination, the prototype and all the S-types have the same characteristic impedance over the entire frequency range. To prove this, I will first derive a formula for the mid-series impedance of the prototype and show that the mid-series impedance of the S-type is the same.

Since the wave-filter may be assumed to extend without limit to the right from AB in Fig. 1, the impedance across the midseries section points A and B will be the same as across the oints A and B. Accordingly we have t e equation The solution of this equation gives This is a general formula and accordingly for the S-type wave-filter we have the equation and substituting from equations (1) and (2), the right-hand member reduces to the same expression as in equation (5). This demonstrates the equality of mid-series characteristic impedance for all S-types and their prototype at all frequencies.

Another important property of S-type wave-filters is that, with their prototype, they all have the same critical frequencies. It is known from the fundamental theory of wave-filters that the critical frequencies lire given by solving for f the two equaions and

i Z2 4 (7) It is-easily shown that if we let fi=0 and and substitute from equations (1) and (2), and simplify, we shall get equations (6) and (7) as the results. Thus we show that the equations that define the critical frequencies are the same for the S-types as for the prototype.

By a parallel course of reasoning which is clearly suggested by the foregoing, it may be shown thatall H-type wave-filters and their prototype have the same midshunt characteristic impedance over the whole frequency range, and that they all.

where F is the propagation constant, de fined as the natural logarithm of the ratio of the current in any series elementto the current in the succeeding J series element. Let Izz-i-ifi, with the conventional notacosha cos fl=1+ 522 andsinh a sin (5:0. It follows that if sinh 01:0, 02:0 and cosh a=1 and Kl 2: cos B 1 This last equation gives the phase relation within the free transmitting ran e. Since cos (5 lies between -1 and +1 it follows that lies between -4 and 0 for the free transwhence z 1 z 2 r in the attenuation range. The full line in 4 is a plot of equation 9, showing a as I a unction of that is, the full line gives the attenuation characteristic of the prototype wave-filter for values of corresponding to frequencies outside the free transmitting range.

For th S-type wave-filter the equation corresponding to equation (9) for various'values of s, we get the dotted line curves as shown in Fi 4.

Thus it appears that -type wave-filter gives a sharper attenuation transltlon than the prototype, on the side beyond Z: the point of maximum attenuation being brought nearer the critical frequency. The attenuation is less sharp, however, beyond this to any desired degree by substituting an S-type wave-filter for the prototype.

oreover, since the characteristic impedance is exactly the same, he can remove a mid-series section or several mid-series sections from the prototype and replace them by S-type sections, -thus making the change of attenuation more abrupt to a degree by combining the attenuation effect of the prototype and its S-type.

On the other hand, if we have a given S- type wave-filter, we may desire that its attenuation shall be less sharp, or that at a remote part of the attenuation range, the attenuation shall be increased; to secure these results we can change the value of s in appropriate manner.

I will now disclose a specific example in which the substitution of S-type sections improves the operation of certain wave-filters. It is well known to make a long telephone circuit available not only for the ordinary telephoning frequencies but also for carrier currents of higher frequency which may be modulated for additional telegraph or telephone uses. At the receiving station mitting range. On the other hand, if sin i h {'1' +1 5*) (10) :0, a=o 0r aw, a cos t= and 4 1 z Substitutin from equations (1) (2) and cosh i (1 (9) this re uces to sinh 48% sinha .(11) I I 1 -9 z,+4z, 1+' a Pl tti the foregoing expression for a, as than beyond. Hence as a general proposifunctlon f tlon if one has a wave-filter giving a cerit becdmes necessary to separate the frequencics so that those of the ordinary telephone range may go to an ordinary telephone receiving instrument and those of h gher frequency ma go to proper modulating apparatus. In ig. 5 the incoming line from the left branches to two wave-filters in paral-' lel which lead respectively to the apparatus J and K, J for ordinary telephone frequencies, K for higher frequencies. Leading to J is a low-pass wave-filter and to K is a high-pass wave-filter. It is desirable that frequencies below 2800 per second go to J, and that higher frequencies go to K. To insure that frequencies in one range shall not go into the other apparatus from that for which they are intended, there must necessarily be an intermediate band of lost frequencies, which it is desirable to make as narrow as possible. It is practicable with my apparatus to put frequencies up to 2600 into J and above 3000 into K, thus having a lost frequency band of only 400 cycles.

The low-pass wave-filter leading to J has series impedances 2, represented by the inductances L At the input end this lowpass wave-filter has ac-series termination, which means that the terminal series impedence is 00 times that of the sections that follow, 00 being less than 1. At the drop end is a reactance annulling network, which comprises a half of an S-type section. I shall refer to this kind of reactance annulling network more fully in connection with Figs. 9 and 10.-

The high-pass wave-filter leading to apparatus K has the series impedances a, represented by the 'reactances of condensers C except that at the input end the value is modified to give the same az-series termination as for the low-pass wave-filter, and at the drop end to give a similar reactance annulling network. In order that each of the two Wave-filters shall co-operate for the intended purpose in this case, they are made complementary, which means that, with the primed letters referring to the high-pass wave-filter.

z",=az, and

Equations (12) give the condition for complementary constant-7c wave-filters in general. wave-filters, these equations following: 7

and

of these conditions.

Equations (13) afford the data by which the values of'C' and L are expressed in terms of C and L in the legends of Fig. 5. In this particular case I let 45:3.87 8.

Though the example now under consideration relates to acase of a simple low-pass wave-filter and a simple high-pass wave- -filter, it is only an example of a general method of treatment which is good for'any pair of complementary constant-7c filters. It will be seen that the values for a, and 2' in equations (12) satisfy the definition of constantK, namel K zz z The attenuation c aracteristics for the low-pass wave-filter and high-pass wavefilter of Fig. 5 are shown res ectively in Figs. 6 and 7 by means of full lines. It is at once apparent that it will be advantageous if these characteristics can be made steeper for each wave-filter. complished by substituting S-type sections between the dotted lines E and F in Fig. 5. The resultant pair of wave-filters is illustrated in Fig. 8, where the substituted S- type sections stand between the lines E and F. It will not be necessary to explain all the details of my design. I have chosen certain parameters so as to make the number This is ac-' of different sizes of inductance coils and condensers as low as practicable, and I have been influenced by other considerations.

Fig. 8 shows the structural modification made in Fi 5 to get a sharper cut-ofi for each wavelter, and the dotted curves in and z,,:0.712 a t-3.16 z, for the low pass wave-filter. For the high pass wave-filter z',,=0.31-6 2' and z" ,=0.712 2 ,+3.16 2' whence the values appearing as legends on Fig. 8 may be derived.

The foregoing example illustrates how upon inspection of the attenuation char acteristic of a Wave-filter, I can remove a.

section from it and substitute an S-type section to sharpen the cut-off, if so desired. The effect ma be enhanced by substituting a plurality o S-type sections. The value of '8 can be determined with reference to the desired degree of steepness of attenuation characteristic, or with reference to convenience of structural design, or with reference to other conditions, or two or more I will now turn to another example of the application of the theory of S-types for improving the operative characteristic of termination is a .we have the relation which the un a wave-filter. From equation 5 it is apparent that in the free transmitt' range, the mid-series characteristic impe ance of a wave-filter is a pure resistance, remembering that the impedances a, and a, may be regarded practically as pure reactances. Inasmuch as the characteristic impedance of most lines is practically indistinguishable from a pure resistance, the property just mentioned would indicate that a mid-series proper one for a wavefilter so that it may fit a .line without reflection losses. However, it is likely to be the case that the mid-series characteristic impedance, even though a pure resistance over the free transmltting range of he kn uency, is widely variable over that range.

nearly constant over at least the major part of the ran' e. If I should substitute a full S-type sectlon for any section of the wave filter, it would not help matters, because as- I have already explained, the salient property of S-type sections is that they have the same characteristic impedance as the proto- Accordingly, I try the efi'ect of adding at: the end'of the wave-filter a half S-type section as illustrated at the left in Fig. 9, thus terminating the wave-filter at mid-shunt S-type. Now a midishunt termination gives a pure resistance for the characteristic impedance of the wave-filter in the free transmitting range. This may readily be proved according to a procedure that is suggested by the preceding derivation of equation 5. Hence the wave-filter of Fig. 9 has its impedance reduced to a pure resistance, and it remains to investigate the variability of that resistance over the free transmitting range. To do this, the parameter a must be given some particular value'between 0 and 1. A somewhat different way of looking at the diagram of Fig. 9 will be convenient. The two series impedances 0.5 82 and 0.5 2,

.at the left may be looked upon as the wseries impedance of an w-series termination with the first shunt member as a susceptance annulling network. This leaves in the .free transmitting range a resistance l/C where Cg, is the characteristic conductance of the m-series termination. Accordingly whence Substituting for s in terms of a: from equation (14) wefet the legends of Fig. 10, for etermined parameter is now :1:

instead of a.

which may vary from to 1 consistently with the limits for s. Plotting the conductance coefiicient G k, where k 'J l fl. against over the free transmitting range, which we ow 1s terminated at 0 and 4, we get a ifi'erent values of a), one WhlCh makes 0,,

variety of curves in Fig. 11 correspondin to bviously it would be desirableto have 1t (1 I' am sketching the procedure only in outline. I mention it here merely as one of several examples of a plications of my improved S-type method It will be sufficient for the present purpose, that for constant 70 types the most available value of a; is approximately this end half section, besides giving impedance correction in the free transmitting range, has the steeper attenuation charac- O.809. It may be added that teristics of an S-type in the attenuation I range.

Briefly stated, the following aspect of the theory of Figs. 9 and 10 may be helpful. By introducin a half S-type section at the end I lose not ing as compared with ordinary mid-series termination of the wavefilter, and I introduce a parameter .9, substituted by as, with freedom to choose for w the value which gives the most nearly constant impedance over the whole free transmitting range.

Still another example of my improved method ofmodifyin the operative characteristics of a wavedesign of a tapered wave-filter, which I will now discuss. To prevent reflection losses it is always desirable that when a wave-filter is interposed between two lines or piecesof apparatus, the input charac teristic impedance, the characteristic impedance of the wave-filter, and the output characteristic impedance shall be equal or nearly equal. But it does not always happen that the two lines or pieces of apparatus to be united by the wave-filter have their characteristic impedances equal. For example, it may be deslred to receive current from a circuit in a cable, through a wave-filter, and transmit it thence to an 0 en wire line. In such a case the input an output impedances will be unequal. One way of meeting this diificulty is to employ a tapered seem upon first consideration that there would be no advantage in substituting a series of small reflections for a single large reflection; but, when it is remembered that, in general, the currents in the successive sections of the wave-filter differ in phase, it will at once be appreciated that the various little reflections differing in hase will to a large extent neutralize see other, just as the vector sum of a plurality of nonparallel vectors will be much less than if they have the same direction. The improvement is a matter of degree and is small in certain special cases, namely at frequencies for which the phase constant is zero or nearly zero for successive sections of the wave-filter. But in general, the advantage of a tapered wave-filter will be realized. However, the change in characteristic impedance from sect-ion to section must be accomplished in some such way as to avoid changing the critical frequencies or otherwise spoiling the wave-filter action.

Let the input characteristic impedance be Z and the output characteristic impedance be Z and assume that there will be n midscries sections of tapered wave-filter interposed between the terininals. Accordingly there will be 02 1 points of discontinuity; and the continued product of the impedance ratios across these 11. 1 points should be Z /Z and these ratios should be as nearly equal as practicable. A tapered wave-filter that answers to the requirements of the situation here sketched is shown in Fig. 12, where the series impedances are e ual and havethe values except for the ha f value at the mid-series termination; and the shunt impedances have the values appearing as legends in the diagram, a, beingthe initial shunt impedance. It should be understood that z, and 2 have the proper values so that in a wave-filter of uniform sections they would give it a suitable characteristic impedance.

To present the theory of the tapered wavefilter of Fig. 12 I will first direct attention to a hypothetical. design shown in Fig. 13 that stands in an intermediate relation between Figs. 1 and 12. The first mid-series section of Fig. 13 is the same as of Fig. 1, beginning at AB in Fig. 1. -With this as a prototype, the mid-series section in Fig. 13

between G and H is of S-type, where and t has a suitable value based on the ratid said ratio. The next-section from H to is. of S-type, where For the next section and soon. According to the rinciples that have been enunciated, the mi -series charac teristic impedance of the wave-filter of Fig. 13 is throughout thesame as of the prototype Fig. 1. v

It is well understood that if all the im pedances of a net connectin two points are multiplied by the same rea factor, the resultant impedance of the net beween those two points will be multiplied by thatsame factor. Accordingly the mid-series characteristic impedance of Fig. 13 will be stepped up by the factor tat the-mid-series point G if all the impedance elements to the right of G, both series and shunt, are multiplied by t. Again, the mid-series characteristic impedance will he stepped up at H by multiplying all. the impedances to the right of H by t, superposing this operation on the result of the operation of the precedin sentence. Let this procedure be followe clear through to the end of the wave-filter of Fig. 13, and it will be transformed into the wave-' filter of Fig. 14, which is at once seen to be the same as Fig. 12. This derivation of the tapered wave-filter of Fig. 12 through Figs. 13 and 14 from Fig. "1 proves that they:

have the same points of critical frequency and that the resultant wave-filter answers to the taperingrequirement of the situation;

by a proper choice of t, its, resultant impedance ratio will correspond to the given ratio Z The resultant wave-filter has the, advantage that it keeps the number of different sizes of coils and condensers as low as practicable. It will be noticed that the tion, but aconstant ratio is convenient and c appropriate.

Other tapered wave-filters are shown in Figs. 15, 16and 17. In Fig. 15, t 1, and a "the wave-filter is derived from its prototype through the S-type construction, taking s. -t initially. In Fig. 16 t 1, but the theory, of H-type is employed in this case.

The prototype wave-filter ,with the appro-'- 1 parison and contrast with the wave-filter points 0 D. The result of passing to H type sections after the full mid-shunt section, taking gives the series admittances in order,

division point by t,W6 get the resultant Wave-filter of Fig. 16. Its properties and advantages will be apparent upon comof Fig. 12. a

In view of the explanation that has been given for other examples, it is thought that the derivation of the wave-filter of Fig. 16 will be apparent; it is based on H-types, with hzl/t initially.

Wave-filters or wave filter sections of S-type are based on mid-series points as the division points between sections; and

. H-type wave-filters and wave-filter sections are based on mid-shunt points as the division points between sections. These are the only mid-points at which a wave-filter can be divided into sections. These are the only points that divide the wave-filter symmetrically. They are the only points that W111 divide it so that in the simple wave-filter of Fig. 1 the impedance is the same looking either way from the division point. Both the .S-type and the H-type may be looked upon as species under a more generic concept mid-type, which I call the M-type.

I define the class M-type to comprehend the classes S-type and I-I-type, and no others; having precisely defined the S-type and the H-type 1n connection with the foregoing equations 1, 2, 3 and 4, this statement gives an exact definition of the M-type.

It maybe noted that the prototype ltself is a member of the whole of a class of M- types. For example, the prototype is an S-type for which 8:1 and the prototype is an H-type for which h::1. Thus when I refer to a set of wave-filters or wave-filter sections which are all S-types or H-types or M-types of, a common prototype, it will be seen that the prototype itself may be one of the set. It can readily be shown that with a given prototype, the S-type and H-type wave-filters have identical propagation constants provided sh=1.

I claim:

1. A wave-filtenhaving one or more halfsections of a certain kind and one or more other half-sections that are M-types, thereof, M being difl'erent from unity.

2. A wave-filter having its sections and half-sections so related that they comprise different M-types of a common prototype,

having several values for respectively different sections and half-sections.

3. A wave-filter having one or more half-' sections of a-certain kind and one or more half-sections introduced from a different wave-filter having the-same characteristic impedance and the same critical frequencies and a difl'erent attenuation characteristic outside the free transmitting range.

4. A wave filter having recurrent sections and comprising means to give it a steep attenuation characteristic, said means comprising at least one section with component impfdances different from the others and wit the same critical frequencies.

5. A wave filter having recurrent sections and having means to make it cut 013? the transmission abruptly at an end of a transmitting range consisting of at least onehalf section of M-type, M being difierent from unity.

6. A wave filter of the kind having recurrent sections and comprising means to give it a steep attenuation characteristic consisting of a section of M-type, M being different from unity.

7. A tapered wave-filter having its sections all M-types of a common prototype, modified by successively increasing the component impedance elements in the same ratio beyond successive points of junction of the wave-filter sections.

8. A wave-filter having its characteristic impedance at successive mid-section points graded between difi'erent terminal values, and having certain impedance elements of constant value throughout thesections.

9. A wave-filter of tapering impedance having its'sections all M-types of a common prototype, except'forthe variation of impedance from one to another.

10. Two complementary wave-filters connected to the same line, and each comprisin a respective M-type section, M being di erent rom unity.

'11. In combination, a transmission line,

a]; 1} in m! 1 a high p asxe wai e -i il terfconnectd cent to" its fi-eq iencj, Mjbeing di f a low pass wave-filter connected; thereto, fereni; from'unity;

said two wave-filters havingnearlythe same In testimonywhereof, I have. signed my 10 1 critical frequency with narrow le t f name to this, specification this'13th day of '5 quency range between them, andeach said, 8-m1 y,"1921,-- L

; "wave-filter comprising an M-type'section to I i v steepen its attenuation, characteristic adja f "i 1 I OTTO J. ZOBEL 

